Magnesium alloy with Long-Period Stacking Ordered Structure (LPSO) and α-Mg (ordinary HCP structure) phase is expected for a new structural material due to its excellent mechanical properties. Its materials strengthening arises from the kink band formation in LPSO phase and the grain refinement of α-Mg phase in the vicinity of LPSO phase because of recrystallization. In the present study, a multiscale and multiphysics computation for the dynamic recrystallization in α-Mg phase is carried out by coupling the dislocation-based crystal plasticity model for HCP crystals proposed previously by the authors with the multi-phase-field model through dislocation density. In the present model, not only the environmental temperature-dependences of nucleation and nucleus growth but also a pinning effect of boundary migration of recrystallized grain boundary owing to existence and influence of additive elements are newly taken into account. Furthermore, grain size behaviors of recrystallized nuclei are investigated for various volume fractions of additive element and ratios of grain boundary segregation.